Plasma Physics Reports, Vol. 31, No. 7, 2005, pp. 616–620. Translated from Fizika Plazmy, Vol. 31, No. 7, 2005, pp. 667–672.Original Russian Text Copyright © 2005 by Azizov, Kravchenko, Solodovnikov.

LOW-TEMPERATURE PLASMA

The Properties of High-Current High-Pressure DischargesÉ. A. Azizov, S. A. Kravchenko, and S. G. Solodovnikov

Troitsk Institute for Innovation and Fusion Research, Troitsk, Moscow oblast, 142090 RussiaReceived September 14, 2004

Abstract—The properties of high-current high-pressure gas discharges (I = 60 kA, p = 1 atm, τ1/2 = 1.6 ms,r ~ 10 cm) just before the end of the discharge are investigated experimentally. It is shown that the anomalouslyhigh rate of gas cooling after the current is switched off is related to the turbulent hydrodynamic processesinduced by the Rayleigh–Taylor instability at the discharge boundary in the stage of volume radiative coolingof the discharge channel. The turbulent thermal conductivity is estimated using experimental data on the recov-ery of the electric strength of the discharge gap. © 2005 Pleiades Publishing, Inc.

1. INTRODUCTION

Direct measurements of free high-current high-pres-sure discharges have shown that the rate of electric-strength recovery (ESR) in the discharge gap after thecurrent is switched off exceeds the rate of diffusion pro-cesses [1, 2] by several orders of magnitude. This effectfinds a natural explanation in the case of low-pressure(p < 0.1 atm) low-current (I < 1 A) discharges, in whichthe plasma is highly nonequilibrium [3] and the fastESR is provided by volume recombination. However,the higher the pressure and current, the closer theplasma is to equilibrium, and at p ~ 1 atm and I ~ 103 A,the plasma state is usually close to a local thermody-namic equilibrium (though it somehow depends on thegas mixture composition) [3]. For discharges with suchhigh values of p and I (they are generally called high-current high-pressure discharges), the electric strengthis recovered due to the cooling of the entire mass of thegas heated during the discharge. In the absence of cur-rent and any other forced action (e.g., forced air cool-ing), the cooling of the gas in the discharge channel isdetermined by the state of the gas itself before the cur-rent is switched off. Hence, it is necessary to examinethe discharge structure and the related physical pro-cesses just before the end of the discharge. In this paper,we present and analyze the results of such investiga-tions.

The preextinction stage can be conveniently exam-ined by considering so-called “subsonic” free dis-charges with a characteristic current growth rate ofdI/dt ~ 108 A/s [4]. In such discharges, the hydrody-namic flow velocities are lower than the speed of sound,the ponderomotive forces are of minor importance, andthe gas pressure is quite uniform. Under certain condi-tions, a cylindrically symmetric discharge with a fairlywide current-carrying channel can be produced. Thisallows one to use probe diagnostics; as a result, the reli-ability of the results obtained increases significantly.

“Slow” discharges display features characteristic ofsteady-state free arcs, which are dominated by turbu-

1063-780X/05/3107- $26.00 0616

lent convection at the interface with a cold ambient gas.Such convection disturbs the shape of the discharge andsignificantly complicates its inner structure [5].

In discharges with high current growth rates (dI/dt ≥1010 A/s), nonlinear hydrodynamic phenomena relatedto the formation of intense shock waves become impor-tant and instabilities caused by the high magnetic pres-sure arise [6].

2. EXPERIMENTAL SETUP AND MEASUREMENT TECHNIQUE

A schematic of the experimental setup is shown inFig. 1. The discharge is supplied from capacitor bank C,which is connected to the discharge circuit via spark gapSG. Inductance L serves to form a current pulse ofrequired duration. The discharge chamber is a sealedstainless-steel cylinder with a diameter of 46 cm. Alongits axis, two electrodes in the shape of truncated coneswith major and minor diameters of 70 and 55 mm areinstalled. At the side wall of the chamber, there are open-ings for probe diagnostics and four viewing windows.

The discharge was ignited by exploding a 0.1-mm-diameter copper wire set between the electrodes alongtheir axis. Special experiments showed that perturba-tions introduced during such ignition into the dischargestructure rapidly decayed. Thorough studies of anotherignition technique with the use of a slipping arc dis-

R

LC

P

Fig. 1. Schematic of the experimental setup.

© 2005 Pleiades Publishing, Inc.

THE PROPERTIES OF HIGH-CURRENT HIGH-PRESSURE DISCHARGES 617

charge [7] showed that the discharge features werealmost similar to those observed in our study.

The discharge current was measured using a coaxialshunt, and the arc voltage was measured using a resis-tive divider. The spatial distribution of the magneticfield generated by the discharge current was measuredby magnetic probes, and the electric field was measuredby double passive electric probes (see [8] for details).

The total radiation energy emitted from the dis-charge was measured with a calorimeter, and the timeevolution of the emission intensity was determinedwith the use of an electrodynamic shutter.

The discharge was photographed with a fast framingcamera through the viewing windows of the dischargechamber. The arc plasma temperature was determinedfrom spectral measurements by the method of relativeintensities.

The ESR process was studied using a double activeelectric probe by a method similar to that used in [1].The measurements began after the discharge currentwas switched off. The voltage applied to the two probeelectrodes was increased until either the probe currentor the voltage reached its critical value, Im or Um,respectively. As either of these critical values wasachieved, the voltage abruptly (over a time much lessthan its rise time) dropped to zero. After a certain pauseneeded for the relaxation of the excessive chargearound the probe, the voltage was increased again. Thisprocess was repeated many times. The time duringwhich the envelope of the voltage pulses arrived at theplateau U = Um was identified as the time tu required forthe recovery of a given electric strength unambiguouslydetermined by the Um value. The cutoff current Im waschosen such that the energy deposited by the probevoltage pulses was much smaller than the energy storedin the plasma. An electronic circuit enabling such analgorithm is described in detail in [9].

The measurements were performed in the centralcross section (equally distant from the discharge elec-trodes). The probe electrodes were set parallel to thedischarge axis at the same distance r from it. The bareends of the electrodes made of 1-mm-diameter wirewere separated by a distance of z = 2 cm. In our exper-iments, the critical values of the probe voltage and cur-rent were Um = 18 kV and Im ≈ 2 mA, respectively.

The value of tu depends on the gap length z. For z <7 mm, an electric breakdown of a cold gas occurred.For z ≥ 1 cm, the scatter in the times during which theenvelope of the voltage pulses arrived at the plateau didnot exceed the measurement error (~10%). This effectmay be attributed to the fact that the distribution of theelectric field between the probe electrodes is highlynonuniform. The field is maximum near the electrodesand depends slightly on the distance between them ifthis distance is much larger than the probe radius.

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3. EXPERIMENTAL RESULTS

Our experiments were performed at C = 1.6 × 10–2 Fand L = 1.6 × 10–5 H. The initial stored energy was70 kJ, the active resistance of the discharge circuit wasR = 1.5 × 10–2 Ω , and the interelectrode distance was12 cm. The working gases were nitrogen and air atatmospheric pressure. The inner structure and current–voltage characteristics of electric discharges in thesegases are very similar. Thereafter, unless otherwiseindicated, the results from experiments with nitrogenare presented.

The data obtained with two fast framing camerasoriented at a right angle to one another in the plane per-

600

0 400

U, V

t, µs800 1200 1600

450

300

150

0

72

36

0

I, kA

Fig. 2. Waveforms of discharge current and voltage.

50

2 6

σ, Ω–1 cm–1

r, Òm

40

30

20

10

04

1 2 3 456

Fig. 3. Radial profiles of the discharge plasma conductivityσ(r, t) at t = (1) 300, (2) 400, (3) 500, (4) 600, (5) 700, and(6) 800 µs.

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pendicular to the chamber axis show that the glowingpart of discharge is nearly cylindrical in shape and itsradius increases in time. The axial symmetry of the dis-charge is also confirmed by the data from magneticprobes installed in the same plane at an angle of 120° toone another.

Figure 2 shows waveforms of the discharge currentand voltage. The shape of the current pulse is close to asinusoid with an amplitude of 60 kA and a half-periodof 1.6 ms. The voltage spike at the initial instant isattributable to the breakdown caused by the explosionof the copper wire. At t ~ 300 µs, the voltage decreasesto 240 V and remains almost constant up to t ~ 1000 µs.After this, it gradually decreases and then drops to zerotogether with the current.

The data from magnetic and passive electric probeswere used to determine the time evolution of the radial

10

2

r, cm

t, 10–4 s

8

6

4

2

4 6 8 10

2

3

1

Fig. 4. Time evolution of the boundaries of plasmas withdifferent conductivities: σ = (1) 0.9σmax, (2) 0.2σmax, and

(3) 2 × 10–6σmax where σmax = 55 Ω–1 cm–1.

1.0

0 0.4

Radiation energy, rel. units

t, ms0.8 1.2 1.6

0.5

Fig. 5. Total radiation energy emitted from a discharge vs.time.

profile of the plasma conductivity σ(r, t) (Fig. 3). Thetime evolution of the plasma boundaries with differentσ values is shown in Fig. 4. The upper curve wasobtained by estimating the conductivity near the elec-trodes of a passive electric probe at the instant when theprobe signal appeared [8].

In an equilibrium plasma, the conductivity is a func-tion of state: for a fixed pressure, there is a one-to-onerelation between the conductivity and temperature. Inour case, the discharge core conductivity of σmax =55 Ω–1 cm–1 corresponds to a temperature of T ≈13000 K. This is in good agreement with the resultsfrom spectroscopic measurements, according to whichthe temperature of the copper vapor at the dischargeaxis is T ≈ 12500 K.

Figure 5 shows the total radiation energy emittedfrom the discharge as a function of the time elapsedfrom the beginning of the discharge. The radiationenergy is normalized to the energy measured by the cal-orimeter without a shutter when the discharge currentflows for only during one half-period.

Figure 6 illustrates the dynamics of the ESR processfor different rates with which the current was switchedto the shunt connected in parallel to the discharge [1].Curve 1 corresponds to a relatively fast (over a time ofabout 100 µs) switching at the instant of the currentmaximum, whereas curve 2 corresponds to a relativelyslow decrease in the current during the natural develop-ment of the discharge. The electric strength of 15 kV iscompletely recovered over 4 ms and over about 8 msafter the fast and slow switching-off of the current,respectively.

The radial profile of the time required for the recov-ery of the electric strength of air when the current isswitched off slowly is shown in Fig. 7. As wasexpected, the ESR rate is maximum at the dischargeperiphery and minimum at the center. For r ≤ 4 cm, thisdependence has an explicit plateau.

4. DISCUSSION OF THE RESULTS

An analysis of the data from Figs. 2 and 3 shows thatthe transient processes related to discharge ignitiondecay almost completely by the time t ~ 300 µs. Start-ing from this instant, the discharge can be conditionallydivided into three regions: central, intermediate, andperipheral. In the central region (r ≈ 3–4 cm), the cur-rent density; the electric conductivity; and, accordingly,the temperature are nearly constant over space andtime. The main variations in the current density andelectric conductivity occur in the intermediate region,whereas in the peripheral region, the temperaturedecreases to the temperature of the cold ambient gas.The dimensions of all the regions increase with time.The peripheral region expands much faster than thecentral one (see Fig. 4). The contributions from differ-ent transfer mechanisms can be estimated using theHellenbaas–Heller energy balance equation. It follows

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THE PROPERTIES OF HIGH-CURRENT HIGH-PRESSURE DISCHARGES 619

from these estimates that, in the central region, the mainfraction of the deposited Joule energy is carried awayby freely escaping radiation [8], whereas in the inter-mediate region, the energy is mainly lost by heat con-duction. A significant fraction (~50%) of the radiationemitted from the central region is absorbed in theperipheral region. The main mechanism for the arcexpansion in this region is convection; i.e., it is relatedto the hydrodynamic flow of a relatively cold gas.

The behavior of a discharge in the current-rise stagewas described in [10–13], which were devoted to themodeling of discharges with a current-carrying channeltransparent to its own emission. In those papers, a self-consistent analytic physical model was developed thatpredicted all the most important discharge parameters(the electric field, the temperature, and the radius andthe expansion rate of the current-carrying channel) forany growth rate of the discharge current and withoutmaking any additional assumptions about the tempera-ture dependence of the transport coefficients. It wasshown that, for each working gas, there is a region inthe (I, dI/dt) phase plane that corresponds to a universalself-regulating regime of arc operation to which the dis-charge evolves, whatever the initial conditions were. Aconsequence of such self-regulation is stabilization ofthe discharge parameters: as the current increases byone order of magnitude, the temperature and the elec-tric field vary by only a few tens of percent.

In the current-rise stage, a regime is established inwhich Joule heating and radiative cooling nearly bal-ance one another. A decrease in the current is accompa-nied by a decrease in the energy deposition; this leadsto a decrease in the temperature due to volume cooling.However, volume radiative losses may dominate in theenergy balance only at relatively high temperatures. Inatmospheric-pressure nitrogen at T < 8000–9000 K,this effect is almost absent. This is confirmed by directcalorimetric measurements of the total radiation energyemitted from the discharge (see Fig. 5). As wasexpected, radiative losses are most intense in the cur-rent-rise stage and near the current maximum and thenrapidly decrease to zero.

Simple estimates show that, for laminar flows, thecharacteristic cooling time of a gas column with adiameter of about 10 cm and an initial temperature of8000 K is a few tenths of a second. Hence, the observedESR rate can be attributed only to turbulent hydrody-namic processes.

The reason for such turbulent mixing can be theonset of Rayleigh–Taylor instability at the interfacebetween the cold and hot gases. Radiative cooling ofthe current-carrying channel after the current isswitched off causes intense reverse gas flow. As thetemperature decreases, the emission power reduces tozero and the motion of the cold gas towards the centerslows down. As a result, the inertia force directedtoward the center arises. This force is similar to theforce of gravity exerted by a heavy gas on an underlying

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light gas. In this case, the gradients of the pressure anddensity are oppositely directed. This provokes thedevelopment of the Rayleigh–Tailor instability, whichleads to the generation of, first, laminar and, then, vor-tex flows of the cold gas into the hot one. Finally, theflow pattern becomes chaotic; i.e., the turbulent mixingof the hot and cold gases occurs.

The process of cooling depends on which harmonicsdominate during the onset of instability. When thetranslational energy of the cold gas is transformed intothe lower harmonics with a wavelength on the order ofthe channel radius, the instability substantially disturbsthe geometry of the discharge and leads to its fragmen-tation. If the energy is transferred to short-wavelengthperturbations, then heat transfer immediately becomes

15

0 2

U, kV

t, ms4 6 8

5

10 1 2

Fig. 6. ESR dynamics for two different decay rates of thedischarge current.

12

0 2

tu, ms

r, cm4 6 12

2

10

8

6

4

8 10

Fig. 7. The radial profile of the time tu, needed for recover-ing the electric strength of air in the case where the dis-charge current was switched off slowly.

620 AZIZOV et al.

diffusive in character and the effective thermal conduc-tivity λeff substantially exceeds its classical value.

The linear stage of this process was considered in[14]. The velocity of the reverse flows v and, conse-quently, the instability growth rate γ depend on the ini-tial plasma temperature and the current decay rate.Under the conditions corresponding to curve 1 inFig. 6, the velocity v reaches a few hundred meters persecond and the deceleration is dv /dt ~ 106 m/s2, whichis 105 times higher than the gravitational accelerationnear the Earth’s surface. The gas density varies by twoorders of magnitude, and the growth rate of the lowerharmonics is γ ~ 104 s–1.

Let us estimate λeff using the data from Fig. 7 andassuming that the gas cooling in the final stage of ESRis diffusive in character. The insufficient measurementaccuracy did not allow us to resolve variations in theESR rate in the central region (rc ≈ 4 cm). When coolingis caused by diffusion, the inner region is always cooledmore slowly than the outer one. Hence, the time τ ofheat diffusion through the central region is no longerthan the experimental error δtu ~ 1 ms in determining

the ESR time. On the other hand, we have τ ~ Cpρ/λby definition, where Cp and ρ are the specific heatcapacity and specific density of the gas, respectively.From this, we obtain the lower estimate for the sought

quantity: λeff ~ Cpρ/δtu ≈ 1 W/(cm K), which is morethan 100 times higher than the thermal conductivity ofair in the temperature range in which ESR begins (i.e.,at T < 4000 K).

5. CONCLUSIONS

In this study, the properties of high-current high-pressure gas discharges have been examined using anoptimal experimental model. The model incorporatesall the features characteristic of the preextinction stageof high-current high-pressure discharges, whereas allthe side effects hampering direct measurements andtheir interpretation are excluded.

The experimental results have revealed the mainfeatures of a discharge in the current rise stage. Theavailable literature data on the mechanisms responsiblefor the spatiotemporal structure of a discharge are con-tradictory. This is partially explained by the fact that theuse of optical methods for determining the radial pro-files of the arc parameters is impeded by the largeuncertainty in the spectral characteristics of the work-ing mixture and by the difficulty of accounting for theabsorption of radiation in cold gas layers. The fairlylarge dimensions of the discharge produced allowed usto use probe diagnostics, which, together with high-speed photorecording, calorimetric measurements, andparallel measurements of the gas temperature by therelative intensities of the spectral lines, furnished aclear insight into the discharge. With these data, it ismuch easier to study the decay stage, which begins

rc2

rc2

immediately after the current is switched off, becausethe initial conditions of the problem are well defined.

An analysis of the data obtained has shown that theanomalously high cooling rate of the gas stems prima-rily from the fact that, at the very beginning of the cool-ing process, the radiation escapes from the centralregion of the discharge within a relatively short timeinterval. Thereafter, the instability that develops at theinterface between the hot and cold gases provokes theirturbulent mixing.

The data obtained have lain the basis for the devel-opment of an adequate physical model of the dischargedecay. Hopefully, further experimental studies in com-bination with theoretical analysis and numerical simu-lations will provide a deeper insight into this compli-cated phenomenon.

The results obtained go beyond the scope of gas dis-charge physics and are related to an important branch ofcontemporary hydrodynamics—turbulent mixing.They can also be applied to the development of newtypes of arc switches.

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Translated by N.N. Ustinovskiœ

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